Random walk on a 100-point circle

Points $0,1,\dots,99$ are arranged in order around a circle. A walker starts at point $1$ and at every step moves to one of its two neighbours, each with probability $\tfrac12$. What is the expected number of steps until the walker first reaches point $0$?

$99$. Cut the circle at $0$: the walker sits $1$ step from $0$ one way and $99$ steps the other way. For a symmetric simple walk between barriers at distances $a$ and $b$, the expected exit time is $ab$, here $1\times 99$.